Exam 5: Probability Distributions

If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types, we can use hypergeometric distribution. If a population has A objects of one type, while the remaining B objects are of the other type, and if n objects are sampled without replacement, then the probability of getting x objects of type A and n - x objects of type B is $P ( x ) = \frac { A ! } { ( A - x ) ! x ! } \cdot \frac { B ! } { ( B - n + x ) ! ( n - x ) ! } \div \frac { ( A + B ) ! } { ( A + B - n ) ! n ! }$ In a relatively easy lottery, a bettor selects 4 numbers from 1 to 14 (without repetition), and a winning 4-number combination is later randomly selected. What is the probability of getting all 4 winning numbers?

Write the word or phrase that best completes each statement or answers the question -An experiment of a gender selection method includes a control group of 8 couples who are not given any treatment intended to influence the genders of their babies. Construct a table listing the possible values of the random variable x (which represents the number of girls among the 8 births)and the corresponding probabilities. Then find the mean and standard deviation for the number of girls in such groups of 10 and the maximum and minimum usual values for the number of girls. Round all results to four decimal places.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $n = 30 , x = 12 , p = 0.20$

Solve the problem. -In a certain town, 44% of voters favor a given ballot measure. For groups of 31 voters, find the variance for the number who favor the measure.

Solve the problem. -In a certain town, 60 percent of voters are in favor of a given ballot measure and 40 percent are opposed. For groups of 360 voters, find the mean for the number who oppose the measure.

Solve the problem. -The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 15. Find the mean for the number of seeds germinating in each batch.

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$ . -The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than .4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 418 jawbreakers that weigh more than .4 ounces?

Identify the given random variable -The number of freshmen in the required course, English 101

If the random variable x has a Poisson Distribution with mean µ = 0.604, find the probability that x = 1.

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. -In a certain town, 70% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults)who have a college degree. () 0 0.0081 1 0.0756 2 0.2646 3 0.4116 4 0.2401

Identify the given random variable -The height of a randomly selected student

Provide an appropriate response. -List the three methods for finding binomial probabilities in the table below, and then complete the table to discuss the advantages and disadvantages of each. Methods Advantage Disadvantage

Solve the problem. -A die is rolled 7 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$ . -A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 541 consumers who recognize the Dull Computer Company name?

Solve the problem. -The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. Find the variance for the probability distribution. () 1 0.16 2 0.19 3 0.22 4 0.21 5 0.12 6 0.10

Find the standard deviation, ?, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. -n = 2661; p = .63

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2? -n = 1104, p = 0.93

Let the random variable x represent the number of heads in five flips of a coin. Construct a table describing the probability distribution, then find the mean and standard deviation.

Find the probability of at least 2 girls in 10 births. Assume that male and female births are equally likely and that the births are independent events.

Find the standard deviation, ?, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $n = 25 ; p = 3 / 5$